<h2>题目编号 : 245</h2>
<div style="color:#666;font-size:80%;">15 May 2009</div><br />
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<p>We shall call a fraction that cannot be cancelled down a resilient fraction.<br /> Furthermore we shall define the resilience of a denominator, <var>R</var>(<var>d</var>), to be the ratio of its proper fractions that are resilient; for example, <var>R</var>(12) = <img src="" style="display:none;" alt="^(" /><sup>4</sup><img src="" style="display:none;" alt=")" />&frasl;<img src="" style="display:none;" alt="_(" /><sub>11</sub><img src="" style="display:none;" alt=")" />.</p>


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<td>The resilience of a number <var>d</var> <img src='images/symbol_gt.gif' width='10' height='10' alt='&gt;' border='0' style='vertical-align:middle;' /> 1 is then</td>
<td><div style='text-align:center;'>&phi;(<var>d</var>)<br /><img src='images/blackdot.gif' width='36' height='1' alt='' /><br />
<var>d</var> - 1</div></td><td>, where &phi; is Euler's totient function.</td>
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<td>We further define the <b>coresilience</b> of a number <var>n</var> <img src='images/symbol_gt.gif' width='10' height='10' alt='&gt;' border='0' style='vertical-align:middle;' /> 1 as <var>C</var>(<var>n</var>)</td><td>=&nbsp;</td>
<td><div style='text-align:center;'><var>n</var> - &phi;(<var>n</var>)<br />
<img src='images/blackdot.gif' width='54' height='1' alt='' /><br />
<var>n</var> - 1</div></td><td>.</td>
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<tr><td>The coresilience of a prime <var>p</var> is <var>C</var>(<var>p</var>)</td>
<td>=&nbsp;</td>
<td><div style='text-align:center;'>1<br /><img src='images/blackdot.gif' width='34' height='1' alt='' /><br /><var>p</var> - 1</div></td><td>.</td>
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<p>The resilience of a number <var>d</var> <img src='images/symbol_gt.gif' width='10' height='10' alt='&gt;' border='0' style='vertical-align:middle;' /> 1 is then <font "size=4"><img src="" style="display:none;" alt="^(" /><sup>&phi;(<var>d</var>)</sup><img src="" style="display:none;" alt=")" />&frasl;<img src="" style="display:none;" alt="_(" /><sub>(<var>d</var>-1)</sub><img src="" style="display:none;" alt=")" /></font>, where &phi; is Euler's totient function.</p>

<p>We further define the <b>coresilience</b> of a number <var>n</var> <img src='images/symbol_gt.gif' width='10' height='10' alt='&gt;' border='0' style='vertical-align:middle;' /> 1 as <var>C</var>(<var>n</var>) = <font "size=4"><img src="" style="display:none;" alt="^(" /><sup>(<var>n</var> - &phi;(<var>n</var>))</sup><img src="" style="display:none;" alt=")" />&frasl;<img src="" style="display:none;" alt="_(" /><sub>(<var>n</var> - 1)</sub><img src="" style="display:none;" alt=")" /></font>.
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<p>The coresilience of a prime <var>p</var> is <var>C</var>(<var>p</var>) = <font "size=4"><img src="" style="display:none;" alt="^(" /><sup>1</sup><img src="" style="display:none;" alt=")" />&frasl;<img src="" style="display:none;" alt="_(" /><sub>(<var>p</var> - 1)</sub><img src="" style="display:none;" alt=")" /></font>.</p>
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<p>Find the sum of all <b>composite</b> integers 1 <img src='images/symbol_lt.gif' width='10' height='10' alt='&lt;' border='0' style='vertical-align:middle;' /> <var>n</var> <img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' /> 2<img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' />10<img src="" style="display:none;" alt="^(" /><sup>11</sup><img src="" style="display:none;" alt=")" />, for which <var>C</var>(<var>n</var>) is a <dfn title="A fraction with numerator 1">unit fraction</dfn>.
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<p class="info"> Note: the upper limit has been changed recently. Check out that you use the right upper limit.</p>

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